Redundancy of looped water distribution networks is quantified with expected shortage, a reliability surrogate which can represent frequency, duration and severity of damages caused by failures of components. Based on this surrogate and its variations (total expected shortage and allowable shortage fraction), two optimization models that lead to the determination of minimum cost pipe diameters to provide specific levels of reliability are developed: the expected shortage optimization model (ESOM), and the allowable shortage fraction optimization model (ASFOM). Studied are comprehensively two aspects of these basic models: computational time and flexibility to satisfy sophisticated design conditions. Because the two basic models are too large to be of practical use in most cases, a modification (CBCM) that heuristically omits many constraints is constructed and its behavior explored. Minor variations of these models are also developed to demonstrate the flexibility which is inherent in the basic structure. This flexibility permits the satisfaction of special real-world design conditions that result in specific reliability requirements at particular nodes. Another variation (OMET) is capable of sizing a storage facility in addition to determining optimal pipe diameters. These models have successfully been applied to the optimization of example networks. The application results noted that a reliability surrogate of expected shortage is very useful in optimizing networks with constrained redundancy and applicational limitations of the models to practical problems in terms of computational time and flexibilities are avoidable. Especially, the results show that the models have the power to undertake direct exploration of tradeoffs between cost and reliability.